4K, 2K, 5K, etc., are rough expressions of display and camera resolutions. They are an approximate count of the number of pixels the device can render along the long edge of its image rectangle. Thus, 4K resolution is approximately 4,000 pixels wide. 2K (which accounts for most of the digital projectors we're used to seeing in theaters) has about half that number of pixels along the same edge, so the image projected has half the detail. The RED cameras that Jackson shot with are capable of 5K capture resolution, but there currently aren't any commercial projectors (that I'm aware of) that will display that resolution.

A chart of the newer 4K projectors and displays now commonly available can be found in the Wikipedia article on 4K resolution. Man is but an ass if he go about to expound this dream.